A new approach for computationally efficient estimation of stability factors for
parametric partial differential equations is presented. The general parametric bilinear
form of the problem is approximated by two affinely parametrized bilinear forms at
different levels of accuracy (after an empirical interpolation procedure). The successive
constraint method is applied on the coarse level to obtain a lower bound for the stability
factors, and this bound is extended to the fine level by adding a proper correction term.
Because the approximate problems are affine, an efficient offline/online computational
scheme can be developed for the certified solution (error bounds and stability factors) of
the parametric equations considered. We experiment with different correction terms suited
for a posteriori error estimation of the reduced basis solution of
elliptic coercive and noncoercive problems.

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